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Perhatikan gambar di bawah ini! Pada persegi panjang ABCD , diketahui u = DC .dan v = BC . Diketahui BP : PC = 1 : 3 dan DQ : QC = 1 : 2 . Maka PQ ​ = ...

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Pada persegi panjang , diketahui .dan . Diketahui  dan . Maka  ...

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D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

adalah .

 stack P Q with rightwards arrow on top adalah 3 over 4 v with rightwards arrow on top minus 2 over 3 u with rightwards arrow on top.

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Diberikan persegi panjang ABCD, dengan dan . Perbandingan , maka panjang . Perbandingan , maka panjang , sehingga . Diketahui .dan , dengan demikiandidapatkan : Jadi, adalah .

Diberikan persegi panjang ABCD, dengan stack B P with rightwards arrow on top plus stack P C with rightwards arrow on top equals stack B C with rightwards arrow on top dan stack italic D italic Q with rightwards arrow on top plus stack italic Q C with rightwards arrow on top equals stack italic D C with rightwards arrow on top.

Perbandingan stack B P with rightwards arrow on top space colon space stack P C with rightwards arrow on top equals 1 space colon space 3, maka panjang stack P C with rightwards arrow on top equals fraction numerator 3 over denominator 1 plus 3 end fraction stack B C with rightwards arrow on top equals 3 over 4 stack B C with rightwards arrow on top.

Perbandingan stack D Q with rightwards arrow on top space colon space stack Q C with rightwards arrow on top equals 1 space colon space 2, maka panjang stack Q C with rightwards arrow on top equals fraction numerator 2 over denominator 1 plus 2 end fraction stack D C with rightwards arrow on top equals 2 over 3 stack D C with rightwards arrow on top, sehingga stack C Q with rightwards arrow on top equals 2 over 3 stack C D with rightwards arrow on top.

Diketahui u with rightwards arrow on top equals stack D C space with rightwards arrow on top.dan v with rightwards arrow on top equals stack B C with rightwards arrow on top, dengan demikian didapatkan :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell stack P Q with rightwards arrow on top end cell equals cell stack P C with rightwards arrow on top plus stack C Q with rightwards arrow on top end cell row cell stack P Q with rightwards arrow on top end cell equals cell 3 over 4 stack B C with rightwards arrow on top plus 2 over 3 stack C D with rightwards arrow on top end cell row cell stack P Q with rightwards arrow on top end cell equals cell 3 over 4 v with rightwards arrow on top plus 2 over 3 open parentheses negative u with rightwards arrow on top close parentheses end cell row cell stack P Q with rightwards arrow on top end cell equals cell 3 over 4 v with rightwards arrow on top minus 2 over 3 u with rightwards arrow on top end cell end table end style 

Jadi, stack P Q with rightwards arrow on top adalah 3 over 4 v with rightwards arrow on top minus 2 over 3 u with rightwards arrow on top.

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